Abstract:
It is now well-known that fractional quantum numbers can arise as the
collective excitations of a many-body system. The canonical example of
such
fractionalization is a 2D electron gas placed in a transverse magnetic
field
in the fractional quantum Hall (FQH) regime. It is understood that the
Coulomb
interaction between electrons is crucial to stabilize the incompressible
FQH
ground state. The system is strongly correlated in the sense that its
many-
body wavefunctions cannot be constructed from the single-particle states
of
the constituent fundamental degrees of freedom. The questions then
naturally
arise whether strong correlations, thus defined, or a broken
time-reversal
symmetry is necessary for fractionalization to happen. I will argue in
this
talk, by describing two recent theoretical proposals, that the
answers
to both questions are negative. Some implications of these proposals for
topological schemes of quantum computation are briefly discussed.